Backstepping quasi-continuous high-order sliding mode control for a Takagi-Sugeno fuzzy system with an application for a two-link robot control

A new control scheme is proposed for motion tracking of a Takagi-Sugeno fuzzy system using the backstepping quasi-continuous high-order sliding mode (HOSM) control technique. First, a Takagi-Sugeno fuzzy model is used to represent the original second-order nonlinear system; most of the parameters for this model can be computed offline. Next, a conventional backstepping sliding mode control (BSMC) is designed to stabilize and guarantee the exact motion tracking for the Takagi-Sugeno fuzzy system. However, use of the conventional sliding mode control generates significant chattering. Therefore, a quasi-continuous second-order sliding mode (QC2S) control is employed to reduce chattering and obtain higher tracking precision, resulting in a backstepping quasi-continuous second-order sliding mode (BQC2S) control law. Combining the Takagi-Sugeno fuzzy model with the BQC2S controller results in a controller scheme that preserves the advantages of both techniques, such as the low online computational burden of the Takagi-Sugeno fuzzy model, and the low chattering, robustness, and fast transient response of the BQC2S controller. Finally, the proposed controller is used to control a two-link robot manipulator and is compared with the existing approaches. Simulation results are presented to demonstrate the effectiveness of the proposed methodology.